personaly I would not.
A varmint bullet is made to rapidly expand on contact. It may not make it through the chest wall. Especally with a shoulder hit.
If you are going to take only neck shots..... maybe.
With that said I have seen a deer or two taken with 22 Hornet and 222 Rem that a center chest hit was devistating and turned the lungs in to goop tha had older varmint style bullets in them. Also the 22 Hornet and the 222 Rem do not hit more than 2700 FPS with 45 grain bullets and I think the 3,000 + of your 22-250 will have the bullet flying apart more. i once was watching a guy shoot a 22-250 with really small bullets at warp speed 3,900+ and every now and then the bullets would not make it to the 100 yard mark, other times it would show up as shrapnell on the target. Watching the bullet in the spotting scope we realized it was hitting bugs on the range and the bullet was exploding. perfect for a ground squirrel or Ground hog but may just wound a deer. Replace it with a soft point of some kind, slow down the load a little, and i think you are in business.
I once read a Capstick article about a guy shooting a hot 378 Weathery mag adn they shot a Zebra at 50 or 75 yards. the bullet was going so fast it just blew up on impact and a hole about the size of a baseall in the zebra. When the Zebra ran out to 300 yards the bullet has slowed to 375 H&H point blank speeds and worked perfectly.
Hey Dale,
I was digging through my desk today and I found a Swede and a Mauser 7mm/ Us 30-06 stripper clip in a draw with your name on a post it with "get directions and send".
What was I supose to do?